Haem-copper oxidase (HCO) catalyses the natural reduction of oxygen to water using a haem-copper centre. Despite decades of research on HCOs, the role of non-haem metal and the reason for nature's choice of copper over other metals such as iron remains unclear. Here, we use a biosynthetic model of HCO in myoglobin that selectively binds different non-haem metals to demonstrate 30-fold and 11-fold enhancements in the oxidase activity of Cu- and Fe-bound HCO mimics, respectively, as compared with Zn-bound mimics. Detailed electrochemical, kinetic and vibrational spectroscopic studies, in tandem with theoretical density functional theory calculations, demonstrate that the non-haem metal not only donates electrons to oxygen but also activates it for efficient O-O bond cleavage. Furthermore, the higher redox potential of copper and the enhanced weakening of the O-O bond from the higher electron density in the d orbital of copper are central to its higher oxidase activity over iron. This work resolves a long-standing question in bioenergetics, and renders a chemical-biological basis for the design of future oxygen-reduction catalysts.